Question

any1 remember the trapazoid and simpsons rule for integrals??

Answer 1

Trapezoidal rule is:
A method of finding an approximate value for an integral, based on finding the sum of the areas of trapezia. Suppose we wish to find an approximate value for ∫ab f(x)dx. The interval a≤x≤b is divided up into n sub-intervals, each of length h=(b − a)/n, and the integral is approximated by ½h(y0+2y1+2y2+...+2yn−1+yn),where yr=f(a+rh). This is the sum of the areas of the individual trapezia, one of which is shown in the diagram. The error in using the trapezium rule is approximately proportional to 1/n2, so that if the number of sub-intervals is doubled, the error is reduced by a factor of 4.

Answer 2

Simpson Rule is:

Also known as parabolic rule. A basic approximation formula for definite integrals which states that the integral of a real-valued function ƒ on an interval [a,b] is approximated by h[ƒ(a) + 4ƒ(g + h) + ƒ(b)]/3, where h = (b - a)/2; this is the area under a parabola which coincides with the graph of ƒ at the abscissas a, a + h, and b. A method of approximating a definite integral over an interval which is equivalent to dividing the interval into equal subintervals and applying the formula in the first definition to each subinterval.

Answer 3

thanks!